Alan Turing's 1950s tiger stripe theory proved

Feb 19, 2012

Researchers from King's College London have provided the first experimental evidence confirming a great British mathematician's theory of how biological patterns such as tiger stripes or leopard spots are formed.

The study, funded by the Medical Research Council and to be published online in Nature Genetics, not only demonstrates a mechanism which is likely to be widely relevant in vertebrate development, but also provides confidence that chemicals called morphogens, which control these patterns, can be used in regenerative medicine to differentiate stem cells into tissue.

The findings provide evidence to support a theory first suggested in the 1950s by famous code-breaker and mathematician Alan Turing, whose centenary falls this year. He put forward the idea that regular repeating patterns in biological systems are generated by a pair of morphogens that work together as an 'activator' and 'inhibitor'.

To test the theory the researchers studied the development of the regularly spaced ridges found in the roof of the mouth in mice. Carrying out experiments in mouse embryos, the team identified the pair of morphogens working together to influence where each ridge will be formed. These chemicals controlled each other's expression, activating and inhibiting production and therefore controlling the generation of the ridge pattern.

The researchers were able to identify the specific morphogens involved in this process  FGF (Fibroblast Growth Factor) and Shh (Sonic Hedgehog  so-called because laboratory fruit flies lacking the fly version have extra bristles on their bodies). They showed that when these morphogens' activity is increased or decreased, the pattern of the ridges in the mouth palate are affected in ways predicted by Turing's equations. For the first time the actual morphogens involved in this process have been identified and the team were able to see exactly the effects predicted by Turing's 60-year-old speculative theory.

Dr Jeremy Green from the Department of Craniofacial Development at King's Dental Institute said: 'Regularly spaced structures, from vertebrae and hair follicles to the stripes on a tiger or zebrafish, are a fundamental motif in biology. There are several theories about how patterns in nature are formed, but until now there was only circumstantial evidence for Turing's mechanism. Our study provides the first experimental identification of an activator-inhibitor system at work in the generation of stripes  in this case, in the ridges of the mouth palate.

'Although important in feeling and tasting food, ridges in the mouth are not of great medical significance. However, they have proven extremely valuable here in validating an old theory of the activator-inhibitor model first put forward by Alan Turing in the 50s.

'Not only does this show us how patterns such as stripes are formed, but it provides confidence that these morphogens (chemicals) can be used in future regenerative medicine to regenerate structure and pattern when differentiating stem cells into other tissues.

'As this year marks Turing's centenary, it is a fitting tribute to this great mathematician and computer scientist that we should now be able to prove that his theory was right all along!'

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User comments : 23

Science does not "Prove" things as you state in your headline. A hypothesis survives a test and remains a good theory or even our best theory. Nothing has ever been proved in the history of science. Please read up on Popper.

While I agree there could be speculation, I would have to beg to differ on science never proving anything. The fact you are typing or reading on here is proof positive that it DOES prove things, and even more, does things with those things it proves.So unless we are all in the stone age, I would say you are incorrect.

wait come to think of it, even in the stone age science solved problems, we just didnt call it science yet...

The fact you are typing or reading on here is proof positive that it DOES prove things, and even more, does things with those things it proves.

Nikola Tesla didn't believe in atoms or electrons, yet he invented the three phase power system based on a hypothesis on electrical fluids that was patently wrong, yet produced applicable results. Analogs work, but they always fail at some point.

You can explain a computer with magic and still produce meaningful results as long as your magic book contains the right ideas on how to make a working transistor.

Science does not "Prove" things as you state in your headline. A hypothesis survives a test and remains a good theory or even our best theory. Nothing has ever been proved in the history of science. Please read up on Popper.

You should read more yourself. Science uses inferential statistics, whereas Popper is talking about logical inferences: both of which entail different epistemologies. For instance, falsification is non-sensical in terms of inferential statistics. If we accept a null-hypothesis, then we are doing so off of a specific probability value (P). In turn, the probability of making a type 2 error is 1-P, i.e., not 0%. Consequently, in a strict sense, logical falsificationism isn't even applicable to science.

Science does not "Prove" things as you state in your headline. A hypothesis survives a test and remains a good theory or even our best theory. Nothing has ever been proved in the history of science. Please read up on Popper.

I am quite interested in what you said. Could you recommend some books on this topic? Thanks a lot.You should read more yourself. Science uses inferential statistics, whereas Popper is talking about logical inferences: both of which entail different epistemologies. For instance, falsification is non-sensical in terms of inferential statistics. If we accept a null-hypothesis, then we are doing so off of a specific probability value (P). In turn, the probability of making a type 2 error is 1-P, i.e., not 0%. Consequently, in a strict sense, logical falsificationism isn't even applicable to science.

@Going I was going to say how wrong you are but Martin Forge already did that for me. I wish people would stop confusing what they learned during their "Logic" and/or "Statistics" courses they took in their Bachelor/Master in Political "Sciences" (or another similar) degree with hard science.

Biological organisms work according to mathematically expressible equations and in mathematics you do have the ability to prove a hypothesis.

Falsification is the only form of assertion does not apply to mathematics.

Does anyone actually understand Turing's theory about this subject, and is it possible to summarise it in some easy to understand form? Or give references for further studying?

Just saying "activators and inhibitors do it" explains nothing at all. In partcular, how do these (entirely in-cell?) activators and inhibitors give a result that depends on the spatial position of the cell in relation to other cells in the tissue?

Visual: Morphogens are literally just anything that causes an effect on tissue growth/development. In general, they work because of concentration differences that occur during development. In this case, FGF and Shh are two of the morphogens (proteins) that, in varying concentration, causes different phenotype in the organism (tigers). Think of a color gradient from Black, to grey, to white (http://www.adobe....ient.jpg is a good example of a gradient.. think of the colors as concentration of the morphogen)

Are mathmatical or science proofs a fleeting thing? I think maybe. Although I steer far from the near religious application that "Nothing has ever been proved in the history of science", I do imagine that existent proofs may not survive the tests of time and space...but then neither shall we.

You can only "prove" things relative to a context defined by initial assumptions.

"Proving" something is relegated to the domain of the following statement "If a, b, and c are true, then d is true", the problem is, you then have to "prove" a, b, and c... and the only way to do that is to say "If x, y, and z are true then a is true"... you cannot ever get away from the initial assumptions, because at the final level the initial assumption is "If my perception of reality is not a complete illusion then..." and there is no way to prove that your perception of reality is not an illusion.

Science does not "Prove" things as you state in your headline. A hypothesis survives a test and remains a good theory or even our best theory. Nothing has ever been proved in the history of science. Please read up on Popper.

Read "The Fabric of Reality" (1997) by Oxford professor David Deutsch for an explanation of how knowledge is created, what can be known and what can't be known.

Though there is, strictly speaking, no such thing as a scientific proof. There is, however, such a thing as a currently scientific best model. But you can show that there is ALWAYS (theoretically) a better model to be had than the current one - with the best 'model' being the universe itself (it - and it alone - fully and accurately represents what it is).

The thing about models is: They are a tradeoff between simplicity and accuracy. While the universe as a model of itself may be very (ultimately) accurate it is also not a model that is simple to use.

What science strives for is to get best models that encompass a lot of what the universe seems to be like - while retaining greatest possible simplicity.

E.g. relativity, quantum mechanics and electrodynamics do a very good job at trading miniscule inaccuracy for enormous ease of use.

Nikola Tesla didn't believe in atoms or electrons, yet he invented the three phase power system based on a hypothesis on electrical fluids that was patently wrong, yet produced applicable results. Analogs work, but they always fail at some point.

You can explain a computer with magic and still produce meaningful results as long as your magic book contains the right ideas on how to make a working transistor.

Yea but the science gives you the capability to see how its really working. No magic necessary. That's my point.

In terms of trying to mathematically prove something, sure. Can't do it. However proof is all around us in a natural form, even if this is an illusion, it is whatever it is. Science is simply a measurement system to try and get as exact as possible to whatever 'it is'.

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